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Simplifying 8x2 + -51x + 71 = 0 Reorder the terms: 71 + -51x + 8x2 = 0 Solving 71 + -51x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 8.875 + -6.375x + x2 = 0 Move the constant term to the right: Add '-8.875' to each side of the equation. 8.875 + -6.375x + -8.875 + x2 = 0 + -8.875 Reorder the terms: 8.875 + -8.875 + -6.375x + x2 = 0 + -8.875 Combine like terms: 8.875 + -8.875 = 0.000 0.000 + -6.375x + x2 = 0 + -8.875 -6.375x + x2 = 0 + -8.875 Combine like terms: 0 + -8.875 = -8.875 -6.375x + x2 = -8.875 The x term is -6.375x. Take half its coefficient (-3.1875). Square it (10.16015625) and add it to both sides. Add '10.16015625' to each side of the equation. -6.375x + 10.16015625 + x2 = -8.875 + 10.16015625 Reorder the terms: 10.16015625 + -6.375x + x2 = -8.875 + 10.16015625 Combine like terms: -8.875 + 10.16015625 = 1.28515625 10.16015625 + -6.375x + x2 = 1.28515625 Factor a perfect square on the left side: (x + -3.1875)(x + -3.1875) = 1.28515625 Calculate the square root of the right side: 1.133647322 Break this problem into two subproblems by setting (x + -3.1875) equal to 1.133647322 and -1.133647322.Subproblem 1
x + -3.1875 = 1.133647322 Simplifying x + -3.1875 = 1.133647322 Reorder the terms: -3.1875 + x = 1.133647322 Solving -3.1875 + x = 1.133647322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1875' to each side of the equation. -3.1875 + 3.1875 + x = 1.133647322 + 3.1875 Combine like terms: -3.1875 + 3.1875 = 0.0000 0.0000 + x = 1.133647322 + 3.1875 x = 1.133647322 + 3.1875 Combine like terms: 1.133647322 + 3.1875 = 4.321147322 x = 4.321147322 Simplifying x = 4.321147322Subproblem 2
x + -3.1875 = -1.133647322 Simplifying x + -3.1875 = -1.133647322 Reorder the terms: -3.1875 + x = -1.133647322 Solving -3.1875 + x = -1.133647322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.1875' to each side of the equation. -3.1875 + 3.1875 + x = -1.133647322 + 3.1875 Combine like terms: -3.1875 + 3.1875 = 0.0000 0.0000 + x = -1.133647322 + 3.1875 x = -1.133647322 + 3.1875 Combine like terms: -1.133647322 + 3.1875 = 2.053852678 x = 2.053852678 Simplifying x = 2.053852678Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.321147322, 2.053852678}
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